Identifiability of an X-Rank Decomposition of Polynomial Maps

Pierre Comon (1) , Yang Qi (2) , Konstantin Usevich (1)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 University of Chicago

In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition. We prove new results on generic/maximal rank and on identifiability of a particular polynomial decomposition model. In the paper, we try to make results and basic tools accessible for general audience (assuming no knowledge of algebraic geometry or its prerequisites).

Mots clés: X-rank; identifiability; polynomial decomposition; Waring decomposition; generic rank

Domaines: Traitement du signal et de l'image [eess.SP]; Géométrie algébrique [math.AG]

Pierre Comon, Yang Qi, Konstantin Usevich. Identifiability of an X-Rank Decomposition of Polynomial Maps. SIAM Journal on Applied Algebra and Geometry, 2017, 1 (1), pp.388-414. ⟨10.1137/16M1108388⟩. ⟨hal-01763858⟩